Problem: $ \left(\dfrac{81}{49}\right)^{-\frac{3}{2}}$
Explanation: $= \left(\dfrac{49}{81}\right)^{\frac{3}{2}}$ $= \left(\left(\dfrac{49}{81}\right)^{\frac{1}{2}}\right)^{3}$ To simplify $\left(\dfrac{49}{81}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{49}{81}$ To simplify $\left(\dfrac{49}{81}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{7}{9}}\right)^{2}=\dfrac{49}{81}$ so $ \left(\dfrac{49}{81}\right)^{\frac{1}{2}}=\dfrac{7}{9}$ So $\left(\dfrac{49}{81}\right)^{\frac{3}{2}}=\left(\left(\dfrac{49}{81}\right)^{\frac{1}{2}}\right)^{3}=\left(\dfrac{7}{9}\right)^{3}$ $= \left(\dfrac{7}{9}\right)\cdot\left(\dfrac{7}{9}\right)\cdot \left(\dfrac{7}{9}\right)$ $= \dfrac{49}{81}\cdot\left(\dfrac{7}{9}\right)$ $= \dfrac{343}{729}$